PairNorm: Tackling Oversmoothing in GNNs (1909.12223v2)

Abstract: The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings indistinguishable. We take a closer look at two different interpretations, aiming to quantify oversmoothing. Our main contribution is PairNorm, a novel normalization layer that is based on a careful analysis of the graph convolution operator, which prevents all node embeddings from becoming too similar. What is more, PairNorm is fast, easy to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GNN. Experiments on real-world graphs demonstrate that PairNorm makes deeper GCN, GAT, and SGC models more robust against oversmoothing, and significantly boosts performance for a new problem setting that benefits from deeper GNNs. Code is available at https://github.com/LingxiaoShawn/PairNorm.

Tackling Oversmoothing in Graph Neural Networks (GNNs)

This paper addresses a fundamental issue in the field of Graph Neural Networks (GNNs), particularly focusing on the phenomenon of oversmoothing. Oversmoothing occurs when repeated graph convolutions lead to similar node embeddings, which can degrade performance as the number of layers increases. The authors propose a novel normalization layer designed to mitigate this problem.

Key Contributions

The primary contribution of this research is the introduction of a normalization scheme, referred to as PairNorm. This normalization is designed to prevent the excessive similarity in node embeddings that characterizes oversmoothing, without altering the architectural framework or introducing additional parameters. PairNorm is applicable across various GNN architectures, including GCN, GAT, and SGC.

Experimental Demonstration: The experiments indicate that PairNorm enhances the robustness of deeper GCN, GAT, and SGC models, significantly improving their performance in scenarios that benefit from increased depth. The authors release the implementation for reproducibility, allowing for further exploration and application of their methodology.

In-depth Understanding of Oversmoothing

The paper provides a detailed examination of oversmoothing by distinguishing between node-wise and feature-wise oversmoothing. Node-wise oversmoothing refers to the convergence of node representations, while feature-wise oversmoothing leads to a homogeneity in features across the network. The authors introduce quantitative measures—row-diff and col-diff—to track these phenomena, using them to substantiate their claims.

Theoretical and Practical Implications

Theoretical Insights: By linking graph convolution operations to graph-regularized least squares, the authors illuminate the inherent smoothing effect of GNNs. This perspective not only clarifies the underlying mechanics of oversmoothing but also guides the development of solutions like PairNorm.

Practical Benefits and Use Case: A practical scenario presented is the semi-supervised node classification with missing vectors (SSNC-MV), where not all nodes have feature vectors. In such cases, deeper GNNs facilitated by PairNorm demonstrate marked improvements in performance by effectively utilizing available neighborhood information to recover missing features.

Future Directions

The insights and methods presented in this paper pave the way for several future research avenues:

1. Exploration of Deeper Architectures: With tools to mitigate oversmoothing, researchers can confidently explore deeper GNN architectures that were previously infeasible due to performance degradation.
2. Broader Applications in Sparse Data Scenarios: The SSNC-MV setting suggests potential applications in other domains facing data sparsity challenges, such as recommendation systems and social network analysis.
3. Further Normalization Techniques: Drawing parallels between normalization in traditional deep learning and GNNs may yield additional innovative normalization techniques suited to the unique properties of graph-structured data.

In summary, this paper presents a significant advancement in addressing the oversmoothing problem in GNNs, enabling more robust performance across deeper models and various graph-based tasks. The introduction of PairNorm represents a practical and theoretically grounded approach to enhancing the versatility and efficacy of GNNs.